truncated icosahedron

Its dual is the truncated icosahedron, an Archimedean solid.

The truncated icosahedron is also hypothesized in geology to be the driving force behind many tectonic fabrics on earth.

Although not a hydrocarbon, fullerene has the shape of a truncated icosahedron, an Archimedean solid.

Paper model truncated icosahedron (association football ball)

Its convex hull is a nonuniform truncated icosahedron.

This polyhedron looks very similar to the uniform truncated icosahedron which has 12 pentagons, but only 20 hexagons.

An truncated icosahedron of frequency 6 has 350 hexagonal faces and 12 pentagonal faces.

The first ball to use a truncated icosahedron design, with 12 black and 20 white patches intentionally used to improve visibility on black-and-white TV sets.

The area A and the volume V of the truncated icosahedron of edge length a are:

This tiling is called a hyperbolic soccerball for its similarity to the truncated icosahedron pattern used on soccer balls.

The truncated icosahedron easily verifies the Euler characteristic:

The design was a truncated icosahedron - essentially a "Geodesic Sphere", consisting of 12 pentagonal and 20 hexagonal panels.

Cartesian coordinates for the vertices of a truncated icosahedron centered at the origin are all even permutations of:

The first fullerene to be discovered was buckminsterfullerene C - an allotrope of carbon with 60 atoms in each molecule, arranged in a truncated icosahedron.

The familiar 32-panel football design is sometimes referenced to describe the truncated icosahedron Archimedean solid, carbon buckyballs or the root structure of geodesic domes.

The most familiar spherical polyhedron is the soccer ball (outside the USA, a football), thought of as a spherical truncated icosahedron.

Most modern footballs consist of twelve regular pentagonal and twenty regular hexagonal panels positioned in a truncated icosahedron spherical geometry.

The balls used in soccer and team handball are perhaps the best-known example of a spherical polyhedron analog to the truncated icosahedron, found in everyday life.

A truncated icosahedron with "solid edges" is a drawing by Lucas Pacioli illustrating The Divine Proportion.

The 32-panel configuration is the spherical polyhedron corresponding to the truncated icosahedron; it is spherical because the faces bulge from the pressure of the air inside.

There are two hexagons and one heptagon on each vertex, forming a pattern similar to a conventional soccer ball (truncated icosahedron) with heptagons in place of pentagons.

The Telstar was the first World Cup ball to use the now-familiar truncated icosahedron for its design, consisting of 12 black pentagonal and 20 white hexagonal panels.

There are four Archimedean solids with 60 vertices: the truncated icosahedron, the rhombicosidodecahedron, the snub dodecahedron, and the truncated dodecahedron.

In geometry, the truncated icosahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids whose faces are two or more types of regular polygons.

The truncated icosahedron has five special orthogonal projections, centered, on a vertex, on two types of edges, and two types of faces: hexagonal and pentagonal.